In this work, we design and produce micron-sized fiber mats by blending poly(ε-caprolactone) (PCL) with small amounts of block copolymers poly(ethylene oxide)m-block-poly(ε-caprolactone)n (PEOm-b-PCLn) using electrospinning. Three different PEOm-b-PCLn block copolymers, with different molecular weights of PEO and PCL, were synthesized by ring opening polymerization of ε-caprolactone using PEO as initiator and stannous octoate as catalyst. The polymer blends were prepared by homogenous solvent mixing using dichloromethane for further electrospinning procedures. After electrospinning, it was found that the addition to PCL of the different block copolymers produced micron-fibers with smaller width, equal or higher hydrophilicity, lower Young modulus, and rougher surfaces, as compared with micron-fibers obtained only with PCL. Neural stem progenitor cells (NSPC), isolated from rat brains and grown as neurospheres, were cultured on the fibrous materials. Immunofluorescence assays showed that the NSPC are able to survive and even differentiate into astrocytes and neurons on the synthetic fibrous materials without any growth factor and using the fibers as guidance. Disassembling of the cells from the NSPC and acquisition of cell specific molecular markers and morphology progressed faster in the presence of the block copolymers, which suggests the role of the hydrophilic character and porous topology of the fiber mats.